mireabulletinRussian Technological JournalRussian Technological Journal2782-32102500-316XRTU MIREA10.32362/2500-316X-2024-12-6-102-112YBOYBLmireabulletin-1035Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGНейронные операторы для гидродинамического моделирования подземных хранилищ газаNeural operators for hydrodynamic modeling of underground gas storage facilitieshttps://orcid.org/0009-0009-9663-6188СиротаД. Д.SirotaD. D.

Сирота Даниил Дмитриевич, заместитель начальника отдела

197229, Санкт-Петербург, Лахтинский пр., д. 2, корп. 3, стр. 1

ResearcherID KUF-1969-2024

Daniil D. Sirota, Deputy Head of Division

2/3, Lakhtinsky pr., St. Petersburg, 197229

ResearcherID KUF-1969-2024

D.Sirota@adm.gazprom.ruhttps://orcid.org/0009-0006-2181-3272ГущинК. А.GushchinK. A.

Гущин Кирилл Андреевич, заместитель начальника Департамента – начальник Управления

197229, Санкт-Петербург, Лахтинский пр., д. 2, корп. 3, стр. 1

Kirill A. Gushchin, Deputy Head of Department – Head of Directorate

2/3, Lakhtinsky pr., St. Petersburg, 197229

K.Gushchin@adm.gazprom.ruХанС. А.KhanS. A.

Хан Сергей Александрович, к.т.н., заместитель начальника Департамента – начальник Управления

197229, Санкт-Петербург, Лахтинский пр., д. 2, корп. 3, стр. 1

Scopus Author ID 27172181100

Sergey A. Khan, Cand. Sci. (Eng.), Deputy Head of Department – Head of Directorate

2/3, Lakhtinsky pr., St. Petersburg, 197229

Scopus Author ID 27172181100

S.Khan@adm.gazprom.ruhttps://orcid.org/0009-0007-7298-3586КостиковС. Л.KostikovS. L.

Костиков Сергей Леонидович, заместитель начальника Управления – начальник отдела

197229, Санкт-Петербург, Лахтинский пр., д. 2, корп. 3, стр. 1

Scopus Author ID 58283384300

Sergey L. Kostikov, Deputy Head of Directorate – Head of Division

2/3, Lakhtinsky pr., St. Petersburg, 197229

Scopus Author ID 58283384300

S.Kostikov@adm.gazprom.ruhttps://orcid.org/0009-0008-3444-2049БутовК. А.ButovK. A.

Бутов Кирилл Андреевич, к.т.н., главный технолог отдела

197229, Санкт-Петербург, Лахтинский пр., д. 2, корп. 3, стр. 1

Kirill A. Butov, Cand. Sci. (Eng.), Chief Technologist of the Division

2/3, Lakhtinsky pr., St. Petersburg, 197229

K.Butov@adm.gazprom.ruПАО «Газпром»РоссияGazpromRussian Federation202405122024126102112Copyright © Сирота Д.Д., Гущин К.А., Хан С.А., Костиков С.Л., Бутов К.А., 20242024Сирота Д.Д., Гущин К.А., Хан С.А., Костиков С.Л., Бутов К.А.Sirota D.D., Gushchin K.A., Khan S.A., Kostikov S.L., Butov K.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.rtj-mirea.ru/jour/article/view/1035Цели

Цели. Значительная часть исследований в области глубокого обучения сосредоточена на изучении отображений между конечномерными пространствами. Гидродинамические процессы фильтрации газа в подземных хранилищах, описываемые дифференциальными уравнениями в частных производных (ДУЧП), требуют изучения отображений между функциональными пространствами бесконечной размерности, что отличает данную задачу от традиционных. Одним из перспективных подходов является построение нейронных операторов – обобщение нейронных сетей для аппроксимации отображений между функциональными пространствами. Цель работы – создание нейронного оператора для ускорения расчетов гидродинамического моделирования подземных хранилищ газа (ПХГ) при допустимых потерях точности.

Методы

Методы. В работе построен и обучен модифицированный нейронный оператор Фурье для гидродинамического моделирования процессов фильтрации газа в ПХГ.

Результаты

Результаты. Показано, что данный метод может быть успешно применен для задач трехмерной фильтрации газа в декартовой системе координат на объектах с множеством скважин. Разработанная модель обеспечивает высокое качество при моделировании объектов с неравномерной сеткой дискретизации и сложной геометрией, несмотря на использование в архитектуре алгоритма быстрого преобразования Фурье. При этом нейронному оператору не требуется большой размер обучающей выборки для достижения высокой точности аппроксимации решений ДУЧП, что демонстрируется не только на тестовой выборке, но и на искусственно сгенерированных сценариях с внесением существенных изменений в структуру моделируемого объекта. Обученный нейронный оператор осуществляет моделирование заданного сценария за доли секунды, что, по меньшей мере, в 106 раз быстрее, чем традиционный численный симулятор.

Выводы

Выводы. Построенный и обученный нейронный оператор показал хорошую эффективность в задаче гидродинамического моделирования ПХГ. Полученный алгоритм воспроизводит адекватные решения даже в случае существенных изменений в моделируемом объекте, которых не было в процессе обучения. Все это делает возможным применение данной модели в задачах планирования и принятия решений в отношении различных аспектов эксплуатации ПХГ, таких как оптимальное использование скважин, контроль давления и управление запасами газа.

Objectives

Objectives. Much of the research in deep learning has focused on studying mappings between finite-dimensional spaces. While hydrodynamic processes of gas filtration in underground storage facilities can be described by partial differential equations (PDE), the requirement to study the mappings between functional spaces of infinite dimension distinguishes this problem from those solved using traditional mapping approaches. One of the most promising approaches involves the construction of neural operators, i.e., a generalization of neural networks to approximate mappings between functional spaces. The purpose of the work is to develop a neural operator to speed up calculations involved in hydrodynamic modeling of underground gas storages (UGS) to an acceptable degree of accuracy.

Methods

Methods. In this work, a modified Fourier neural operator was built and trained for hydrodynamic modeling of gas filtration processes in underground gas storages.

Results

Results. The described method is shown to be capable of successful application to problems of three-dimensional gas filtration in a Cartesian coordinate system at objects with many wells. Despite the use of the fast Fourier transform algorithm in the architecture, the developed model is also effective for modeling objects having a nonuniform grid and complex geometry. As demonstrated not only on the test set, but also on artificially generated scenarios with significant changes made to the structure of the modeled object, the neural operator does not require a large training dataset size to achieve high accuracy of approximation of PDE solutions. A trained neural operator can simulate a given scenario in a fraction of a second, which is at least 106 times faster than a traditional numerical simulator.

Conclusions

Conclusions. The constructed and trained neural operator demonstrated efficient hydrodynamic modeling of underground gas storages. The resulting algorithm reproduces adequate solutions even in the case of significant changes in the modeled object that had not occurred during the training process. The model can be recommended for use in planning and decision-making purposes regarding various aspects of UGS operation, such as optimal control of gas wells, pressure control, and management of gas reserves.

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The authors declare that there are no conflicts of interest present.